Chiefly used in more bang for the buck, the colloquial American-English phrase bang for the buck and variants mean value for money, return on an investment.

In this phrase, which was originally used of military spending on nuclear weapons:
– bang denotes a nuclear explosion;
– buck denotes a dollar.

These are the earliest occurrences of the phrase that I have found, in chronological order:

1-: From the column Matter Of Fact, by the U.S. political columnist Stewart Alsop (1914-1974), originally published in the New York Herald Tribune (New York City, N.Y.) of Monday 21^st December 1953—and reprinted, for example, in The Sheboygan Press (Sheboygan, Wisconsin) of Tuesday 22^nd December 1953:

Matter Of Fact
By Stewart Alsop
The Bang and the Buck

Washington—The Eisenhower administration’s defense plans have by now been unofficially but rather completely revealed. Judging from these plans, the Administration expects to perform a miracle.
The present level of defense spending is to be cut back close to $5,000,000,000 in fiscal 1955. And further cuts are to reduce defense spending several more billions by fiscal 1957. At the same time, air striking power and air defense are to be steadily built up, while combat power in other respects is to be maintained. How is this miracle—if it is a miracle—to be performed?
Part of the answer lies in a basic national strategic decision which deserves to be thoroughly understood. As previously reported in this space, the original “new look” by the Joint Chiefs of Staff called for force levels involving an actual increase, rather than decrease, in defense spending in the next fiscal year. In mid-October, when Admiral Arthur Radford, the chairman of the Joint Chiefs, presented this “new look” to a dismayed National Security Council, he made a brief but cogent statement to the council.
He said, in effect, that one major reason why defense costs were so high was that the military planners had never been told what sort of war to plan for. They had to assume that we might be called on to fight a “conventional” war—like the Korean war—in which no atomic weapons were used. If they could assume, instead, that atomic weapons will be used in any future war, this might make a big difference in their plans.
After some discussion, Radford and the other Chiefs were told to have another look, in a new light. The National Security Council did not go so far as to instruct the military leaders to assume that any future war will be an atomic war—we must still be able to deal with “brush fire wars.” But, they were told to assume that, in anything bigger than “brush fire wars,” atomic weapons will be used.
The Joint Chiefs accordingly went back and re-estimated their requirements, on the theory that atomic firepower can be substituted for manpower and conventional firepower. This “bigger bang for a buck” theory was not, to be sure, the only factor in the proposed cutbacks. Capital investment in equipment for the Army and Navy is virtually complete in many categories. The fighting in Korea has ended, and it is also assumed in administration defense plans that this fighting will not begin again, and that several divisions can eventually be withdrawn from the Far East.
There have also been quite genuine manpower and money savings, for which the new civilian team at the Pentagon can take a deserved bow. For example, no less than 153,000 positions have been eliminated from the hitherto sacred tables of organization of the services, without in any way affecting combat power. Similarly, the Air Force, which in the past has been even more disgracefully overstaffed than the Army, now promises to man close to thirty new wings without any large increase in enlistments.
This is all to the good. It is also all to the good that the discredited and essentially political “balanced force concept” has been thrown in the ashcan. Yet the question remains: Is the “bigger bang for a buck” theory—the theory that nuclear firepower can achieve big money and manpower savings—really sound?
The Army which stands to lose more than a third of its current manpower has of course been hardest hit by the revised plans. And the Army contends fiercely that the theory is not sound. The Army view is that nuclear ground warfare demands mobility, and dispersion, which in turn require heavy mechanization and communications as nearly perfect as humanly possible. This means, the Army contends, not fewer men per combat unit, but more men.
Even the Air Force, ostensibly the chief beneficiary of the new planning is not too happy below the top levels. Some thoughtful officers and civilians in the Air Force believe that the basic assumption in the new planning—that any future war which is more than a “brush fire” will be an atomic war—has not been followed to its logical conclusions. It is true that air striking power and continental defense are both to be strengthened—continental defense is to be assigned well over $4,000,000,000 in the next fiscal year. But the doubters claim that these plans are really only inadequate compromises, in view of the needs imposed by growing soviet air-atomic capabilities.
Indeed, there are plenty of informed officials and officers who privately believe that the requirements of the budget came before the requirements of national security when the original “new look” was revised downward. They believe that the “more bang for a buck” theory is an excuse for the cutbacks, rather than a real reason, and that the “buck” came first by an easy margin, with the “bang” a poor second. It is no doubt still too early to judge, before the new defense plans have been thoroughly explained and defined. But as these plans are further unveiled, it may be wise to bear in mind the chicken-or-egg question: which came first, the buck or the bang

2-: From a United-Press story, first published in several U.S. newspapers on Wednesday 30^th December 1953—for example in The Daily Register (Harrisburg, Illinois):

Washington (UP)—Democrats hoisted storm warnings today over the administration’s decision to withdraw two divisions from Korea.
Sens. Richard B. Russell of Georgia, A. S. Mike Monroney of Oklahoma and Paul H. Douglas of Illinois joined in sounding their concern over the possible consequences at this critical moment in the Far East.
They made it plain that the action, and the administration’s whole “new look” military strategy, will be a major issue in the coming session of Congress. […]
[…]
Monroney called for “exhaustive hearings on the entire defense blue-print” to determine “whether we are sacrificing security in this more-bang-for-a-buck new look.”

3-: From Democratic Dissenters, published in The Evening Star (Washington, D.C.) of Thursday 31^st December 1953:

It is regrettable that a man of Senator Monroney’s stature should trade in such phrases as “more bang for a buck.” This is a terribly serious matter. The President is trying to chart a new course which takes account both of the staggering cost of the military effort we have been making and of the potentialities of new weapons.

4-: From AF Emphasis To Aid Texas Economy, by Ernest Conine, published in the San Antonio Express (San Antonio, Texas) of Thursday 7^th January 1954:

Washington, Jan. 6.—The Eisenhower administration’s reported decision to place increasing reliance on atomic air power indicates that the Air Force will continue to play a vital role in the economy of the Lone Star State, observers here have agreed.
[…]
In order to get “more bang for a buck,” increased reliance would be placed on atomic air power and highly-mobile, well-equipped land forces which would replace a huge standing army.

5-: From Eisenhower’s Dream: A Stronger Nation, published in the New Orleans States (New Orleans, Louisiana) of Friday 8^th January 1954:

In his first State of the Union message President Eisenhower […] outlined his domestic program described in advance notices as a dynamic one sure to catch the fancies of the Congress and the American people, and, opportunely, the electors next November. He gave assurances of further tax reductions, a nearly balanced budget, a satisfactory deal for the farmers, a sensible foreign assistance and trade program, more adequate national defense at less cost or as the capital slang is, “more bang for a buck.”

6-: From Employment and Defense; Two Different Concerns, published in the Morning World-Herald (Omaha, Nebraska) of Saturday 9^th January 1954—reprinted from The Wall Street Journal (New York City, N.Y.):

It is not hard to understand the Administration’s concern with unemployment, for the Administration is concerned with the health of the nation’s economy. Thus President Eisenhower’s order to divert some defense contracts to areas having jobless men will be viewed with some sympathy at first glance.
But a second look will show how glaringly wrong it is.
It is wrong because unemployment is one concern of the Administration and defense is quite a different one. The tax dollars that Congress appropriated for defense ought to go for defense, and the most defense that can be got from those dollars is the particular concern of the Defense Department.
There is a catchy phrase around to describe what the Defense Department is trying to do in this regard. They call it “more bang for a buck.”
But one doesn’t get more bang for a buck by saddling the Defense Department with directives which say that certain areas with labor surpluses ought to get preference in contracts over areas which have no labor surplus.
And the buck loses some of its bang when faster tax write-offs are granted certain distressed areas for erection or improvement of plants which other areas are denied.